Calculate the mass of copper deposited when a current of 0.5 ampere was passed through a solution of…

Analysis

To solve this problem, we need to use Faraday’s First Law of Electrolysis, which relates the mass of a substance deposited during electrolysis to the quantity of electricity passed through the electrolyte.

Concept

The formula for Faraday's law is:

Where:

• $m$ = mass of the substance deposited (in grams)
• $M$ = Molar mass of the element (for Copper, $Cu = 64$)
• $I$ = Current (in Amperes) = $0.5\text{ A}$
• $t$ = Time (in seconds) = $45\text{ minutes} \times 60\text{ seconds/minute} = 2700\text{ s}$
• $n$ = Number of moles of electrons transferred (valency of Copper in $CuCl_2$ is $2$, so $n = 2$)
• $F$ = Faraday’s constant = $96500\text{ C/mol}$

Step-by-Step Solution

1. Convert time to seconds: $t = 45 \times 60 = 2700\text{ s}$

2. Determine the quantity of electricity ($Q$): $Q = I \times t$ $Q = 0.5 \times 2700 = 1350\text{ Coulombs}$

3. Determine the moles of electrons: Since $Cu^{2+} + 2e^- \rightarrow Cu$, we need $2$ moles of electrons to deposit $1$ mole of Copper. Total charge required for $1$ mole of $Cu = 2 \times 96500 = 193000\text{ C}$

4. Calculate the mass ($m$): Using the ratio: $\frac{m}{64} = \frac{1350}{193000}$ $m = \frac{64 \times 1350}{193000}$ $m = \frac{86400}{193000}$ $m \approx 0.44766\text{ g}$

Rounding to three decimal places, we get approximately 0.448g.

Conclusion

Comparing our result to the options provided, the calculated mass matches option D.

Exam Tip: Always remember to convert time from minutes to seconds! A common mistake in JAMB Chemistry is forgetting to multiply by 60, which will lead you to an incorrect answer. Also, check the valency of the metal (e.g., $Cu^{2+}$ means $n=2$, $Ag^+$ means $n=1$) before plugging values into the formula.